Comparing different approaches for solving optimizing models with significant nonlinearities

The property of saddle-path instability often arises in economic models derived from optimising behaviour by individual agents. In the case when underlying functional forms are nonlinear, it is likely that the stable and unstable arms defining the saddle-path dynamics will also have nonlinear properties. While closed-form analytic solutions can always be derived for linearised deterministic versions of these models, it will be necessary to use numerical techniques to derive the dynamic properties of calibrated versions of the associated nonlinear models.